It sounds like you're playing chords by plucking strings one at a time. Unless you're playing arpeggios, that's not the best way to do it: Try strumming them all in a row, in a fluid motion. 

Keep in mind that some pick noise is inevitable, even desirable. In the studio, I do everything I can to *emphasize* incidental noises like the pick hitting the strings, the noises made by the flautist clicking the keys, or the vocalist inhaling before singing a line. It's what makes music sound human and relatable. 

Unless you're getting a truly horrifically loud series of clicks when playing, don't worry about it too much. Listen to other players, and you'll hear that, to a point, this is normal and natural. 

However, lighter nylon picks (like the ones put out by Clayton, for example) can mitigate this, as can lighter strings. There are also hybrid silk/steel strings that can give you a softer sound. (I'm guessing you're playing guitar with steel strings; classical guitars with nylon strings are generally not played with a plectrum.) 

Like Matthew wrote [in his answer](http://music.stackexchange.com/questions/624/how-to-prevent-the-noise-my-guitar-pick-makes/634#634), hold the pick more softly and play more gently and subtly. You'll have a better dynamic range, a less percussive sound, and you'll have better control over your instrument. 

You also ask about playing without a pick. Sure, you can do that, but you'll be playing what's known as *fingerstyle* playing, a very different sort of music than strummed guitar. You'll also be wearing down the fingernails on your strumming hand, so you'll want to prepare for that.